log p(X) = 5

log p(Y) = 2

find the value of log XY(p)

I've attempted changing the base of the original equations but am stuck with little idea of how to proceed.

Please clarify your notation. Does "log p(X)", to you, mean \(\log(p(X))\) or \(\log_p(X)\) or \(\log_X(p)\)? That is, what is the base?

Either give us an image of the problem, or explain what it means in words, so we can be sure. Or, use standard notation, with "_" to indicate a subscript.

I'm guessing that you mean:

\(\log_p(X) = 5\)

\(\log_p(Y) = 2\)

\(\log_{XY}(p) = ?\)

If so, do you know the change of base formula?